I only have two groups which makes it pretty easy but I use a different web form for each and default the group in the form.
This is how I did it you can decide if this works for you:
I copied newticket.html to isticket.html and trticket.html
edit one file and change this line
(%GROUPSELSTD%)
and replace with
<input type=hidden name=grp value=group1>
edit the other like this, change this line
(%GROUPSELSTD%)
and replace with
<input type=hidden name=grp value=group2>
Basically one is Group1, next Group2 etc. if you have more.
Now for users to get the correct webform:
**ttxwebserveraddress**/ttx.cgi?cmd=newticket&form=isticket
**ttxwebserveraddress**/ttx.cgi?cmd=newticket&form=trticket
We don't trust our users to bother choosing a group so we use 2 different forms!
Hope this helps!